A metallurgist has an alloy with 10% titanium and an alloy with 20% titanium. He needs 100 grams of an alloy with 17% titanium. How much of each alloy should
Mathematics
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Question
A metallurgist has an alloy with 10% titanium and an alloy with 20% titanium. He needs 100 grams of an alloy with 17% titanium. How much of each alloy should be mixed to attain the 100 grams of alloy with 17% titanium?
1 Answer

1. User Answers jdoe0001
[tex]\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentration\\ amount \end{array}\\ &&&\\ \textit{10\% alloy}&x&0.1&0.1x\\ \textit{20\% alloy}&y&0.2&0.2y\\ &&&\\ mixture&100&0.17&17 \end{array}[/tex]
now, notice, we use the decimal format for the percent, namely 17% is 17/100 or 0.17 and so on
so.... we know, whatever "x" and "y" is, they must add up to 100 grams
thus x + y = 100
and whatever the concentrated amount is, it must add up to 17 grams for the composition
thus 0.1x + 0.2y = 17
[tex]\bf \begin{cases} x+y=100\implies \boxed{y}=100x\\ 0.1x+0.2y=17\\ \\ 0.1x+0.2\left( \boxed{100x} \right)=17 \end{cases}[/tex]
solve for "x", to see how much is needed of the 10% alloy
what about "y"? well, y = 100  x